GetFEM  5.4.2
gmm_least_squares_cg.h
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30 ===========================================================================*/
31 
32 /**@file gmm_leastsquares_cg.h
33  @author Benjamin Schleimer <bensch128 (at) yahoo (dot) com>
34  @date January 23, 2007.
35  @brief Conjugate gradient least squares algorithm.
36  Algorithm taken from http://www.stat.washington.edu/wxs/Stat538-w05/Notes/conjugate-gradients.pdf page 6
37 */
38 #ifndef GMM_LEAST_SQUARES_CG_H__
39 #define GMM_LEAST_SQUARES_CG_H__
40 
41 #include "gmm_kernel.h"
42 #include "gmm_iter.h"
43 #include "gmm_conjugated.h"
44 
45 namespace gmm {
46 
47  template <typename Matrix, typename Vector1, typename Vector2>
48  void least_squares_cg(const Matrix& C, Vector1& x, const Vector2& y,
49  iteration &iter) {
50 
51  typedef typename temporary_dense_vector<Vector1>::vector_type temp_vector;
52  typedef typename linalg_traits<Vector1>::value_type T;
53 
54  T rho, rho_1(0), a;
55  temp_vector p(vect_size(x)), q(vect_size(y)), g(vect_size(x));
56  temp_vector r(vect_size(y));
57  iter.set_rhsnorm(gmm::sqrt(gmm::abs(vect_hp(y, y))));
58 
59  if (iter.get_rhsnorm() == 0.0)
60  clear(x);
61  else {
62  mult(C, scaled(x, T(-1)), y, r);
63  mult(conjugated(C), r, g);
64  rho = vect_hp(g, g);
65  copy(g, p);
66 
67  while (!iter.finished_vect(g)) {
68 
69  if (!iter.first()) {
70  rho = vect_hp(g, g);
71  add(g, scaled(p, rho / rho_1), p);
72  }
73 
74  mult(C, p, q);
75 
76  a = rho / vect_hp(q, q);
77  add(scaled(p, a), x);
78  add(scaled(q, -a), r);
79  // NOTE: how do we minimize the impact to the transpose?
80  mult(conjugated(C), r, g);
81  rho_1 = rho;
82 
83  ++iter;
84  }
85  }
86  }
87 
88  template <typename Matrix, typename Precond,
89  typename Vector1, typename Vector2> inline
90  void least_squares_cg(const Matrix& C, const Vector1& x, const Vector2& y,
91  iteration &iter)
92  { least_squares_cg(C, linalg_const_cast(x), y, iter); }
93 }
94 
95 
96 #endif // GMM_SOLVER_CG_H__
gmm::clear
void clear(L &l)
clear (fill with zeros) a vector or matrix.
Definition: gmm_blas.h:59
gmm::vect_hp
strongest_value_type< V1, V2 >::value_type vect_hp(const V1 &v1, const V2 &v2)
*‍/
Definition: gmm_blas.h:511
gmm_conjugated.h
handle conjugation of complex matrices/vectors.
gmm::conjugated
conjugated_return< L >::return_type conjugated(const L &v)
return a conjugated view of the input matrix or vector.
Definition: gmm_conjugated.h:294
gmm_kernel.h
Include the base gmm files.
gmm::copy
void copy(const L1 &l1, L2 &l2)
*‍/
Definition: gmm_blas.h:977
gmm_iter.h
Iteration object.
gmm::add
void add(const L1 &l1, L2 &l2)
*‍/
Definition: gmm_blas.h:1268